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Probabilistic analysis software for structural seismic response Sjoberg, Brian David

Abstract

The evaluation of seismic reliability of building structures is a complex and computationally expensive process since it requires, at the most fundamental level, the evaluation of the probabilistic dynamic response of a given structure to the stochastic dynamic action of an earthquake. Because of the difficulty of determining the response of a structure in a statistical sense, past estimates of the seismic reliability of existing structures, and typical structural systems, have been largely qualitative in nature. With the movement of many national building codes towards more performance-based design measures, a need was identified for a more quantitative method of evaluating structural reliability under seismic loading. To meet this need, a new software application called PSResponse was developed that gives engineers and researchers the ability to rigorously evaluate the probable effect of a wide range of ground motion characteristics and structural model parameters, each with their own random nature, on the dynamic response of a structure. The mathematical modeling methods forming the foundation of the software architecture were selected following a comprehensive review of random vibration methods and numerical procedures that assessed their suitability for analyzing the probabilistic seismic response of civil engineering structures. That review determined that the frequency-domain based random vibration methods are too restrictive in their inherent assumptions to confidently apply their results to real structures experiencing realistic earthquakes. Instead, a numerical time-history approach incorporating the Monte Carlo method provides a robust, accurate and straightforward means of evaluating the probabilistic response of a structure without regard to the degree of non-linearity in the restoring force, complexity of the structural system, nature of the variability in structural properties or nature of the random excitation process. As part of the software development process, a new algorithm for parameter identification of the well-known BWBN, or Bouc-Wen, hysteresis model was developed, which included a modification to the function controlling pinching behaviour to simplify the parameter identification process. The number of pinching parameters was reduced from six to three, which has the added benefit that the role of each of the three new parameters is more easily understood than the relationship between the six parameters of the original pinching function. Following development of the beta version of PSResponse, two case studies were completed that demonstrated the capabilities of the software as a research and analysis tool. These case studies provided for the first time a probabilistic analysis of the importance of the hysteresis assumption in inelastic analysis, the accuracy of the well-known equal displacement observation in structural dynamics and the relative effect of random structural properties on elastic dynamic response. Results showed that the hysteretic behaviour of a structure needs to be accurately modeled, particularly in shorter natural period structures, to provide an accurate probabilistic description of response and hence a good estimate of seismic structural reliability. Also, the equal displacement principle is valid in the sense that elastic peak displacement provides a generally conservative first approximation of inelastic peak displacement, which in turn results in a generally conservative prediction of reliability. Finally, case study results showed that the characteristics and randomness of ground motion records has a much larger influence than structural randomness on the probabilistic dynamic response of a structure. Therefore, once a suitable seed record has been selected, the peak response probability distributions for a given structural model could be applied to a real structure with reasonable confidence since the assumed level of uncertainty in the structural parameters needs to be only approximately correct. However, for strength related limit state evaluations related to peak response, structural variability still has an important effect.

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